text: Temperature-dependent atomic lattice vibrations, or phonons, can broaden the core level components and attenuate the interference patterns in an X-ray photoelectron diffraction (XPD) experiment. The simplest way to account for vibrational effects is by multiplying the scattered single-photoelectron wave function  by the Debye–Waller factor:
  where  is the squared magnitude of the wave vector variation caused by scattering,
  and  is the temperature-dependent one-dimensional vibrational mean squared displacement of the  emitter. In the Debye model, the mean squared displacement is calculated in terms of the Debye temperature, , as: